Raking-ratio empirical process with auxiliary information learning

Abstract

The raking-ratio method is a statistical and computational method which adjusts the empirical measure to match the true probability of sets of a finite partition. The asymptotic behavior of the raking-ratio empirical process indexed by a class of functions is studied when the auxiliary information is given by estimates. These estimates are supposed to result from the learning of the probability of sets of partitions from another sample larger than the sample of the statistician, as in the case of two-stage sampling surveys. Under some metric entropy hypothesis and conditions on the size of the information source sample, the strong approximation of this process and in particular the weak convergence are established. Under these conditions, the asymptotic behavior of the new process is the same as the classical raking-ratio empirical process. Some possible statistical applications of these results are also given, like the strengthening of the $Z$-test and the chi-square goodness of fit test.

Exponential increase of the power of the independence and homogeneity chi-square tests with auxiliary information

“…This information can also be resulted from an estimation or a learning from an other larger sample under the condition that this sample is large enough. The author gives in [2] the magnitude of minimum size of the sample to be efficient. More formally let suppose a statistician has a if he has at his disposal all values P rA pN q s " pP pA p1q 1 q, .…”

“…This theorem is only a generalization of Theorem 2 in [2] and its proof is an adaptation of the proof of this theorem.…”

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